Angular accelerometers are generally employed to measure the second derivative of angular rotation with respect to time. In certain specialized machine control applications, a measured angular acceleration is often needed as a direct input to a control system. For example, in order to prevent against disturbance from external angular acceleration, disk drive read/write heads generally require a sensor for sensing angular acceleration so that the control system associated therewith may compensate for the severe shock and/or vibrations that may have caused the angular acceleration.
One approach for determining angular acceleration employs an angular velocity sensor to sense angular velocity, and differentiates the sensed angular velocity to determine the angular acceleration. The design for an angular velocity sensor is usually complex, and angular velocity sensors are generally expensive to produce. In addition, the acceleration measuring device typically requires a differentiator which adds to the complexity and overall cost of the device.
Another approach for determining angular acceleration uses a combination of two linear accelerometers mounted to a rigid body for sensing linear acceleration along two respective perpendicular axes. Generally, linear accelerometers employ a mass suspended from a frame by multiple beams. The mass, beams, and frame act as a spring-mass system, such that the displacement of the mass is proportional to the acceleration applied to the frame. The difference in acceleration signals from the two linear orthogonal accelerometers is proportional to the angular acceleration of the rigid body. Linear accelerometers are readily available and easy to use; however, in order to measure angular acceleration while rejecting linear acceleration, the scale factor, i.e., sensitivity or gain, of the two sensors generally must be clearly matched. An example of two discrete linear accelerometers integrated into a single device is disclosed in an article by M. T. White and M. Tomizuka, entitled "Increased Disturbance Rejection in Magnetic Disk Drives by Acceleration Feedforward Control and Parameter Adaptation," published in Control Eng. Practice, Volume 5, No. 6, pages 741-751, dated 1997. The aforementioned article is incorporated herein by reference.
Another approach for an angular accelerometer is disclosed in an article to T. J. Brosnihan et al. entitled "Surface Micromachined Angular Accelerometer with Force Feedback," published in DSC-Vol. 57-2, 1995 IMECE, Proceedings of the ASME Dynamic Systems and Control Division, pages 941-947, ASME, dated 1995. A similar approach is disclosed in U.S. Pat. No. 5,251,484, entitled "ROTATIONAL ACCELEROMETER," which is also incorporated herein by reference. The approach in U.S. Pat. No. 5,251,484 employs a circular hub centrally supported on a substrate and connected to radially disposed thin film spoke electrodes that flex in response to angular acceleration. Rotational acceleration measurement is achieved by using a differential, parallel plate capacitive pick-off scheme in which the flexible spoke electrodes at the periphery of the fixed disk rotate between fixed reference electrodes so that an off-center position of moving electrodes results in a measured differential voltage from which the disk motion is determined. The sensing capability for such an accelerometer is generally limited to the amount of movement of the flexible spoke electrodes.
The aforementioned conventional approaches employs separate input and output contacts for each capacitor plate, which adds to the complexity and cost of the accelerometer. In addition, some of the conventional accelerometers may suffer from errors introduced by rotational acceleration orthogonal to the sensing axis and errors introduced by linear acceleration. It is therefore desirable to provide for a low cost, easy to make and use, angular accelerometer that minimizes error introduction.